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class SudokuSolver: """9x9 sudoku solver""" def __init__(self,question): if not len(question)==81: raise Error() self.buf=question def get_rows(self,x): """O<=x<9""" if x<0 or x>=9: return [] return self.buf[x*9:(x+1)*9] def get_columns(self,x): """0<=x<9""" if x<0 or x>=9: return [] return self.buf[x::9] def get_groups(self,pos): """0<=pos<81""" if pos<0 or pos>=81: print "range error" return [] y=pos/9/3 x=pos%9/3 base=y*27+x*3 return self.buf[base:base+3]+self.buf[base+9:base+12]+\ self.buf[base+18:base+21] def get_pos(self,x): """0<=pos<81""" y=pos/9 x=pos%9 return x,y def prints(self): print self.buf[0:3],self.buf[3:6],self.buf[6:9] print self.buf[9:12],self.buf[12:15],self.buf[15:18] print self.buf[18:21],self.buf[21:24],self.buf[24:27] print "" print self.buf[27:30],self.buf[30:33],self.buf[33:36] print self.buf[36:39],self.buf[39:42],self.buf[42:45] print self.buf[45:48],self.buf[48:51],self.buf[51:54] print "" print self.buf[54:57],self.buf[57:60],self.buf[60:63] print self.buf[63:66],self.buf[66:69],self.buf[69:72] print self.buf[72:75],self.buf[75:78],self.buf[78:81] def count_zero(self,buf): cnt=0 for x in range(len(buf)): if buf[x]==0: cnt=cnt+1 return cnt def solve_single(self): zcnt=self.count_zero(self.buf) for x in range(81): if self.buf[x]==0: buf_set=self.serch_num(x) if len(buf_set)==1: self.buf[x]=buf_set.pop() return zcnt-self.count_zero(self.buf) def serch_num(self,pos): num_buf=self.buf[pos] self.buf[pos]=0 buf=set(range(10)) groups=set(self.get_groups(pos)) columns=set(self.get_columns(pos%9)) rows=set(self.get_rows(pos/9)) allset=groups.union(columns) allset=allset.union(rows) buf=buf.difference(allset) self.buf[pos]=num_buf return buf def solve_row(self): zcnt=self.count_zero(self.buf) for rows in range(9): pos_list=range(rows*9,rows*9+9) buf_set_list=[self.serch_num(pos_list[0])] for x in range(1,9): buf_set_list.append(self.serch_num(pos_list[x])) for x in range(9): buf=buf_set_list[x] nl=set(range(9)) nl.remove(x) for y in nl: if self.buf[pos_list[y]]==0: buf=buf.difference(buf_set_list[y]) if len(buf)==1: if self.buf[pos_list[x]]==0: self.buf[pos_list[x]]=buf.pop() return zcnt-self.count_zero(self.buf) def solve_column(self): zcnt=self.count_zero(self.buf) for column in range(9): pos_list=[column,column+9,column+18] pos_list=pos_list+[column+27,column+36,column+45] pos_list=pos_list+[column+54,column+63,column+72] buf_set_list=[self.serch_num(pos_list[0])] for x in range(1,9): buf_set_list.append(self.serch_num(pos_list[x])) for x in range(9): buf=buf_set_list[x] nl=set(range(9)) nl.remove(x) for y in nl: if self.buf[column+y*9]==0: buf=buf.difference(buf_set_list[y]) if len(buf)==1: if self.buf[column+x*9]==0: self.buf[column+x*9]=buf.pop() return zcnt-self.count_zero(self.buf) def solve_group(self): zcnt=self.count_zero(self.buf) for group in range(9): base=group%3*3+group/3*27 pos_list=[base,base+1,base+2] pos_list=pos_list+[base+9,base+10,base+11] pos_list=pos_list+[base+18,base+19,base+20] buf_set_list=[self.serch_num(pos_list[0])] for x in range(1,9): buf_set_list.append(self.serch_num(pos_list[x])) for x in range(9): buf=buf_set_list[x] nl=set(range(9)) nl.remove(x) for y in nl: if self.buf[pos_list[y]]==0: buf=buf.difference(buf_set_list[y]) if len(buf)==1: if self.buf[pos_list[x]]==0: self.buf[pos_list[x]]=buf.pop() return zcnt-self.count_zero(self.buf) def solve_all(self): ret=self.solve_group() ret=ret+self.solve_row() ret=ret+self.solve_column() ret=ret+self.solve_single() return ret def solve_all_try(self): zcnt=self.count_zero(self.buf) while True: if self.solve_all()==0: break return zcnt-self.count_zero(self.buf) def prints_memo(self): buf=range(81) for i in range(81): if self.buf[i]==0: buf[i]=self.serch_num(i) else: buf[i]=self.buf[i] print buf[0:3],buf[3:6],buf[6:9] print buf[9:12],buf[12:15],buf[15:18] print buf[18:21],buf[21:24],buf[24:27] print "" print buf[27:30],buf[30:33],buf[33:36] print buf[36:39],buf[39:42],buf[42:45] print buf[45:48],buf[48:51],buf[51:54] print "" print buf[54:57],buf[57:60],buf[60:63] print buf[63:66],buf[66:69],buf[69:72] print buf[72:75],buf[75:78],buf[78:81] def solve_te(self): """try&error""" zcnt=self.count_zero(self.buf) backup_buf=self.buf[:] pos=0 set_buf=set(range(10)) for i in range(81): if self.buf[i]==0: if len(set_buf) > len(self.serch_num(i)): set_buf=self.serch_num(i).copy() pos=i for tmp in set_buf: self.buf[pos]=tmp self.solve_all_try() if self.validate(): break if not self.validate(): self.buf=backup_buf[:] return zcnt-self.count_zero(self.buf) def validate(self): for i in range(81): if not self.buf[i]==0: set_buf=self.serch_num(i) if self.buf[i] not in set_buf: return False return True import unittest class UnitTestSudokuSolver(unittest.TestCase): def setUp(self): self.buf=[0,0,0,0,2,0,0,9,0,0,0,0,0,6,3,0,0,8,3,0,0,0,0,8,1,4,0,0,0,0,0, 4,0,8,0,7,0,8,4,0,0,0,6,1,0,1,0,7,0,5,0,0,0,0,0,1,5,9,0,0,0,0,2,9,0,0,4,8,0,0,0, 0,0,2,0,0,1,0,0,0,0] pass def test_group(self): print "solve_group() test" s=SudokuSolver(self.buf) s.prints() print s.solve_group() s.prints() def test_serch_num(self): s=SudokuSolver(self.buf) buf=s.serch_num(3) if 1 not in buf or 5 not in buf or 7 not in buf: self.fail("now:%s expected:%s\n"%(buf,[1,5,7])) if 2 in buf or 3 in buf or 4 in buf or 6 in buf or 8 in buf or 9 in buf: self.fail("now:%s expected:%s\n"%(buf,[1,5,7])) def test_get_groups(self): s=SudokuSolver(self.buf) buf=s.get_groups(3) if not len(buf)==9: self.fail("get_groups(3):%s"%buf) if not min(buf)==0: self.fail("get_groups(3):%s"%buf) if not max(buf)==8: self.fail("get_groups(3):%s"%buf) def test_solves(self): print "test_solves()" s=SudokuSolver(self.buf) s.prints() print s.solve_all_try() print s.solve_te() s.prints_memo() self.assert_(s.validate()) if __name__ == '__main__': unittest.main()
